Draw a sketch of the curves y = sin x and y = cos x at  and find the area of the region enclosed by them and X-axis.


Asked by Topperlearning User | 12th Aug, 2016, 10:30: PM

Expert Answer:

The region is divided into two parts, one from x = 0 to and second from to x = .But the region is symmetric about x=∏/4 so the required area is
2 asterisk times integral subscript 0 superscript pi divided by 4 end superscript C 1 d x
 
2 asterisk times integral subscript 0 superscript pi divided by 4 end superscript sin left parenthesis x right parenthesis d x
2 asterisk times left square bracket negative cos left parenthesis x right parenthesis right square bracket subscript 0 superscript pi divided by 4 end superscript
2 asterisk times left square bracket 1 minus 1 divided by square root of 2 right square bracket
2 minus square root of 2  The required area is 2-square root of 2 s q space u n i t

Answered by  | 13th Aug, 2016, 12:30: AM